Degenerate matter, Schemes and Mind Maps of Physics

Download Degenerate matter and more Schemes and Mind Maps Physics in PDF only on Docsity! Degenerate matter Degenerate matter[1] is a highly dense state of fermionic matter in which particles must occupy high states of kinetic energy to satisfy the Pauli exclusion principle. The description applies to matter composed of electrons, protons, neutrons or other fermions. The term is mainly used in astrophysics to refer to dense stellar objects where gravitational pressure is so extreme that quantum mechanical effects are significant. This type of matter is naturally found in stars in their final evolutionary states, like white dwarfs and neutron stars, where thermal pressure alone is not enough to avoid gravitational collapse. Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. This degeneracy pressure remains non-zero even at absolute zero temperature.[2][3] Adding particles or reducing the volume forces the particles into higher-energy quantum states. In this situation, a compression force is required, and is made manifest as a resisting pressure. The key feature is that this degeneracy pressure does not depend on the temperature but only on the density of the fermions. Degeneracy pressure keeps dense stars in equilibrium, independent of the thermal structure of the star. A degenerate mass whose fermions have velocities close to the speed of light (particle energy larger than its rest mass energy) is called relativistic degenerate matter. The concept of degenerate stars, stellar objects composed of degenerate matter, was originally developed in a joint effort between Arthur Eddington, Ralph Fowler and Arthur Milne. Eddington had suggested that the atoms in Sirius B were almost completely ionised and closely packed. Fowler described white dwarfs as composed of a gas of particles that became degenerate at low temperature. Milne proposed that degenerate matter is found in most of the nuclei of stars, not only in compact stars.[4][5] Concept Degenerate gases Electron degeneracy Neutron degeneracy Proton degeneracy Quark degeneracy Singularity See also Notes References External links If a plasma is cooled and under increasing pressure, it will eventually not be possible to compress the plasma any further. This constraint is due to the Pauli exclusion principle, which states that two fermions cannot share the same quantum state. When in this highly compressed state, since there is no extra space for any particles, a particle's location is extremely defined. Since the Contents Concept locations of the particles of a highly compressed plasma have very low uncertainty, their momentum is extremely uncertain. The Heisenberg uncertainty principle states , where Δp is the uncertainty in the particle's momentum and Δx is the uncertainty in position. Therefore, even though the plasma is cold, such particles must on average be moving very fast. Large kinetic energies lead to the conclusion that, in order to compress an object into a very small space, tremendous force is required to control its particles' momentum. Unlike a classical ideal gas, whose pressure is proportional to its temperature , where P is pressure, V is the volume, N is the number of particles—typically atoms or molecules—kB is Boltzmann's constant, and T is temperature), the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at absolute zero temperature. At relatively low densities, the pressure of a fully degenerate gas can be derived by treating the system as an ideal Fermi gas, in this way , where K depends on the properties of the particles making up the gas. At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by , where K again depends on the properties of the particles making up the gas.[6] All matter experiences both normal thermal pressure and degeneracy pressure, but in commonly encountered gases, thermal pressure dominates so much that degeneracy pressure can be ignored. Likewise, degenerate matter still has normal thermal pressure, but at extremely high densities, the degeneracy pressure usually dominates. Exotic examples of degenerate matter include neutron degenerate matter, strange matter, metallic hydrogen and white dwarf matter. Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons. In metals it is useful to treat the conduction electrons alone as a degenerate free electron gas, while the majority of the electrons are regarded as occupying bound quantum states. This solid state contrasts with degenerate matter that forms the body of a white dwarf, where most of the electrons would be treated as occupying free particle momentum states. Degenerate gases are gases composed of fermions such as electrons, protons, and neutrons rather than molecules of ordinary matter. The electron gas in ordinary metals and in the interior of white dwarfs are two examples. Following the Pauli exclusion principle, there can be only one fermion occupying each quantum state. In a degenerate gas, all quantum states are filled up to the Fermi energy. Most stars are supported against their own gravitation by normal thermal gas pressure, while in white dwarf stars the supporting force comes from the degeneracy pressure of the electron gas in their interior. In neutron stars, the degenerate particles are neutrons. Degenerate gases likely boson thought possible. In the frame of reference that is co-moving with the collapsing matter, general relativity models without quantum mechanics have all the matter ending up in an infinitely dense singularity at the center of the event horizon. (If one uses the UFT Einstein– Maxwell–Dirac system or its generalizations, then the singularity is avoided and one ends up with a quark star, possibly surrounded by an event horizon.) It is a general result of quantum mechanics that no fermion can be confined in a space smaller than its own wavelength, making such a singularity impossible, unless only bosons are present, but there is no widely accepted theory that combines general relativity and quantum mechanics sufficiently to tell us what the structure inside a black hole might be. If bosons can be conclusively ruled out, one possible theory is that constituent particles decompose into strings, forming a structure called a fuzzball. Gravitational time dilation Matter wave Degenerate energy levels Metallic hydrogen Fermi liquid theory 1. Academic Press dictionary of science and technology (https://www.worldcat.org/oclc/22952145). Morris, Christopher G., Academic Press. San Diego: Academic Press. 1992. p. 662. ISBN 0122004000. OCLC 22952145 (https://www.worldcat.org/oclc/22952145). 2. see http://apod.nasa.gov/apod/ap100228.html 3. Andrew G. Truscott, Kevin E. Strecker, William I. McAlexander, Guthrie Partridge, and Randall G. Hulet, "Observation of Fermi Pressure in a Gas of Trapped Atoms", Science, 2 March 2001 4. Fowler, R. H. (1926-12-10). "On Dense Matter" (https://academic.oup.com/mnras/article/87/2/114/1058897). Monthly Notices of the Royal Astronomical Society. 87 (2): 114–122. Bibcode:1926MNRAS..87..114F (http://adsa bs.harvard.edu/abs/1926MNRAS..87..114F). doi:10.1093/mnras/87.2.114 (https://doi.org/10.1093%2Fmnras%2F 87.2.114). ISSN 0035-8711 (https://www.worldcat.org/issn/0035-8711). 5. David., Leverington, (1995). A History of Astronomy : from 1890 to the Present (https://www.worldcat.org/oclc/84 0277483). London: Springer London. ISBN 1447121244. OCLC 840277483 (https://www.worldcat.org/oclc/84027 7483). 6. Stellar Structure and Evolution section 15.3 – R Kippenhahn & A. Weigert, 1990, 3rd printing 1994. ISBN 0-387- 58013-1 7. ENCYCLOPAEDIA BRITANNICA (http://www.britannica.com/EBchecked/topic/105468/Chandrasekhar-limit) 8. Rotondo, M. et al. 2010, Phys. Rev. D, 84, 084007, https://arxiv.org/abs/1012.0154 9. Potekhin, A. Y. (2011). "The Physics of Neutron Stars". Physics-Uspekhi. 53 (12): 1235. arXiv:1102.5735 (https:// arxiv.org/abs/1102.5735). Bibcode:2010PhyU...53.1235Y (http://adsabs.harvard.edu/abs/2010PhyU...53.1235Y). doi:10.3367/UFNe.0180.201012c.1279 (https://doi.org/10.3367%2FUFNe.0180.201012c.1279). 10. Oppenheimer, J.R., Volkoff, G.M., 1939, Phys. Rev. 55, 374, http://journals.aps.org/pr/abstract/10.1103/PhysRev.55.374 Cohen-Tanoudji, Claude (2011). Advances in Atomic Physics (https://web.archive.org/web/20120511023729/htt p://www.worldscibooks.com/physics/6631.html). World Scientific. p. 791. ISBN 978-981-277-496-5. Archived from the original (http://www.worldscibooks.com/physics/6631.html) on 2012-05-11. Retrieved 2012-01-31. See also Notes References Detailed mathematical explanation of degenerate gases (http://ircamera.as.arizona.edu/astr_250/Lectures/Lec17 _sml.htm) Mass-radius diagram of degenerate star types (http://nrumiano.free.fr/Estars/b_holes.html) Retrieved from "https://en.wikipedia.org/w/index.php?title=Degenerate_matter&oldid=909617537" This page was last edited on 6 August 2019, at 14:33 (UTC). Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. External links